Sixth, we are far from the first to suggest functionally defining space or spacetime. [1]} reads Newton's Scholium to the definition in much this way (though [2]} disagrees). Functionalist strategies have also become very visible in the philosophy of non-relativistic quantum mechanics, where [3]} deploys it in his defence of an Everettian interpretation and [4]} in support of wave function monism. Those latter applications differ from ours because they are concerned with recovering three-dimensional physical space. In contrast, spacetime functionalism in QG is commissioned with functionally recovering 4-dimensional spacetime, and so relates to work by [5]}, [6]}, [7]} in the context of classical spacetime physics. For her, something `plays spacetime's role' and thus is spacetime “just in case it describes the structure of inertial frames, and the coordinate systems associated with these” ([6]}). In GR, the metric field performs spacetime's role in this sense and thus is identified with spacetime by her. As the metric may itself not be fundamental but instead emerge from the collective behavior of more fundamental degrees of freedom, she explicitly leaves open the possibility that the realizers of spacetime's functions may themselves not be fundamental [5]}. As the relationship between the fundamental degrees of freedom and the emergent spacetime realizer is left untouched by Knox's inertial frame functionalism, the latter does also not shed any light on it.Cf. [10]} and [11]} for a more detailed discussion of inertial frame functionalism and how it relates to our project.
